Intra-/inter-molecular relaxation

During the photoelectron emission event there are electronic relaxation effects occurring, which are usually divided into intra- and inter-molecular relaxation effects. These effects can be rationalized in a classical picture as follows. An elec-... 

Bock and coworkers104 have determined proton spin-lattice relaxation times for N,N-dideuterioaniline in perdeuteriobenzene and perdeuterioaniline solutions as a function of the concentration and temperature at 260-360 K. The activation energies of the intra- and inter-molecular relaxation rates were of similar magnitude, namely 4.5 and 4.4 kcalmol-1. At 293 K, the rotational correlation time of the aniline molecule in infinitely dilute perdeuteriobenzene solution was approximately half that of the partially deuteriated aniline molecule, namely 3.0 x 10-12 and 6.3 x ICC12 s 1, respectively. In infinitely dilute perdeuterioaniline the rotational correlation time of (V,iV-dideuterioaniline was 19 x ICC12 s. ... 

The pair of interacting nuclei can be in the same or different molecules, leading to intra- and inter-molecular relaxation. Generally, however, nuclei in the same molecule can approach much more closely than those in different molecules so that intra-molecular relaxation is dominant. 

An examination of the terms for intra- and inter-molecular relaxation eqns. (4.22.2 and 4.22.3) shows that (1 /ri)intrais proportional to the time-dependent probability of solute rotation, while (1/Ti)inter is proportional to solvent mobility. Thus specific solute-solvent forces will modify (l/7i)intra as in the example of l,2-dichloroethane ° quoted on p. 493, while (1/Ti)inter should correlate with the self-diffusion coefficients of the solvent. 

For spin-f nuclei, dipolar interactions may be modulated by intramolecular (DF, reorientation etc.) and/or intermolecular (TD) processes. In general, the intra- and inter-molecular processes can produce quite different Tj frequency dispersion curves. In practice, NMR field cycling experiments are often needed to extend the frequency domain from those employed in conventional spectrometers to a lower frequency range (i.e., the kHz regime) for unambiguous separation (and identification) of different relaxation mechanisms. The proton spin relaxation by anisotropic TD in various mesophases has been considered by Zumer and Vilfan.131 133,159 In the nematic phase, Zumer and Vilfan found the following expression for T ... 

Both Ti and T2 relaxations of water protons are mainly due to fluctuating dipole-dipole interactions between intra- and inter-molecular protons [62]. The fluctuating magnetic noise from all the magnetic moments in the sample (these moments are collectively tamed the lattice) includes a specific range of frequency components which depends on the rate of molecular motion. The molecular motion is usually represented by the correlation time, xc, i.e., the average lifetime staying in a certain state. A reciprocal of the correlation time corresponds to the relative frequency (or rate) of the molecular motion. The distribution of the motional frequencies is known as the spectral density function. 

In our further considerations we assume that the components of the relaxation matrix are known in advance. This is a realistic assumption provided that unsaturated NMR spectra are being dealt with. One should note that equation (35) can be used for the description of motion of the system during time spans which are much longer than the typical correlation times for molecular rotation in liquids (about 10-11—10—12 sec). The processes of intra- and inter-molecular exchange which are considered here are characterized by half-life times longer than 10 5 sec. It seems justified to consider these processes independently of molecular rotations, in spite of the fact that they all participate in the relaxation. 

Both intra- and inter-molecular processes, which occur in liquids, affect the relaxation rates of the spin systems involved. Our considerations are concerned with reactions and rearrangements which are characterized by life-times that are appreciably longer than typical correlation times for molecular rotations. The latter are included in the derivation of the equation (35) of motion. It seems, therefore, that the equation should be valid for the description of a spin system during the period between reactions. 

The next issue in the overview of PES involves surfaces of polymer thin films and condensed molecular solids. There are several issues to be mentioned (1) inter-molecular polarization (relaxation) effects and (2) surface sensitivity. First, under (1), the concept of intra-molecular was described above. When molecules... 

A number of processes contribute to relaxation. Intra- or inter-molecular dipole-dipole interactions with nuclei are less efficient for than for due to a dependence of the relaxation rate. Spin rotation processes, which are especially important for small molecules and ions such as ND3, [NOal , and N2, are more effective at higher temperatures. Shielding anisotropy, which is important for linear or planar nitrogen groups, such as in dinitrogen complexes, becomes more effective at higher fields, and paramagnetic impurities present in... 

The interest of studies on relaxation mechanisms of van der Waals complexes is general they may be considered as models for a larger class of unimolecular reactions. The specificity of van der Waals systems relies on the exceptionally weak coupling between intra- and inter-molecular modes, much weaker than typical intra-state coupling in molecules. The time scales for IVR and VP processes are therefore significantly longer and more convenient for real-time experiments. 

Translational self-diffusion. Whereas in bulk nematics, translational self-diffusion modulates only the dipolar interactions between protons on different molecules (i.e. intermolecular interactions), in microdroplets it also modulates intra-molecular dipolar interactions because the director field in a confined geometry is non-uniform. This new relaxation mechanism is called translational diffusion induced rotation (TDIR). Since intramolecular dipolar interactions are generally stronger than intermolecular interactions, translational selfdiffusion represents a much more effective relaxation mechanism in micro-droplets than in bulk nematics. TDIR is also effective at much lower frequencies than diffusion induced modulation of inter-molecular... 

For the selective enhancement of the wanted reaction channel by laser excitation of the reactands the time span At between photon absorption and completion of the reaction is of fundamental importance. The excitation energy n-hw (n = 1,2,...) pumped by photon absorption into a selected, excited molecular level may be redistributed into other levels by unwanted relaxation processes before the system ends in the wanted reaction channel. It can, for instance, be radiated by spontaneous emission, or it may be redistributed by intramolecular radiationless transitions, due to vibrational or spin-orbit couplings onto many other, nearly degenerated molecular levels which, however, may not lead to the wanted reaction channel. At higher pressures collision-induced intra- or inter-molecular energy transfer may... 

In the condensation reaction between a trifunctional alcohol and a difunctional isocyanate, gel formation is marked by significant changes in the velocity and attenuation in the MHz region. The relaxation in the isolated monomers can be ascribed to a combination of intra- and inter-molecular processes. Intermolecular relaxation occurs in the hydrogen-bonded structure formed as a result of hydroxyl interactions. Reaction between the isocyanate and alcohol leads to the possibility of normal mode contributions to the relaxation spectrum and consequent increase in the ultrasonic attenuation. Detailed analysis of the data is difficult because of the complex topography generated by the reaction of di- and tri-functional monomers. This study does however once more illustrate the possibility of using ultrasonic techniques to monitor polymerization processes. 

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